Subgroups — C₃×C₅×#1918 #14274952

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic
8	C₅×#1918	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₅×#107	C₄	1	4	yes	complemented
19	C₃×C₅×#95	—	2	1	no	—
20	C₃×C₅×#95	—	2	1	no	—
21	C₃×#1918	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic
23	C₅×#389	C₂×C₃	1	1	yes	characteristic
24	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
25	C₅×#340	C₂×C₃	1	1	yes	characteristic
26	C₅×#340	C₂×C₃	1	1	yes	characteristic
27	C₅×#340	C₂×C₃	1	1	yes	characteristic
28	C₅×#336	C₂×C₃	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	—	2	1	no	—
30	C₂²×C₃×C₄×C₅	—	2	1	no	—
31	C₂²×C₃×C₄×C₅	—	2	1	no	—
32	C₂²×C₃×C₄×C₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂×C₃×C₅×C₈	—	2	1	no	—
37	C₂×C₃×C₅×C₈	—	2	1	no	—
38	C₂×C₃×C₅×C₈	—	2	1	no	—
39	C₂×C₃×C₅×C₈	—	2	1	no	—
40	C₂×C₃×C₅×C₈	—	2	1	no	—
41	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
42	C₃×C₅×C₄⋊C₄	—	2	1	no	—
43	C₃×C₅×C₄⋊C₄	—	2	1	no	—
44	C₃×C₅×C₄⋊C₄	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	—	4	2	no	—
48	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
49	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₃×C₅×C₄⋊C₄	Q₈	1	2	yes	—
51	C₃×C₄²×C₅	—	2	1	no	—
52	C₃×C₄²×C₅	—	2	1	no	—
53	C₃×C₄²×C₅	—	4	2	no	—
54	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic
55	C₃×#389	C₂×C₅	1	1	yes	characteristic
56	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
57	C₃×#340	C₂×C₅	1	1	yes	characteristic
58	C₃×#340	C₂×C₅	1	1	yes	characteristic
59	C₃×#340	C₂×C₅	1	1	yes	characteristic
60	C₃×#336	C₂×C₅	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₄²×C₅	—	2	1	no	—
69	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
70	C₅×#107	C₃×C₄	1	4	yes	complemented
71	C₅×#95	—	2	1	no	—
72	C₅×#95	—	2	1	no	—
73	#1918	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
74	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	—	2	1	no	—
76	C₂×C₃×C₄×C₅	—	2	1	no	—
77	C₂×C₃×C₄×C₅	—	2	2	no	—
78	C₂×C₃×C₄×C₅	—	2	2	no	—
79	C₂×C₃×C₄×C₅	—	2	2	no	—
80	C₂×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₃×C₄×C₅	—	2	1	no	—
82	C₂×C₃×C₄×C₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	4	1	no	—
84	C₂×C₃×C₄×C₅	—	4	1	no	—
85	C₂×C₃×C₄×C₅	—	4	1	no	—
86	C₂×C₃×C₄×C₅	—	4	1	no	—
87	C₂×C₃×C₄×C₅	—	4	1	no	—
88	C₂×C₃×C₄×C₅	—	4	1	no	—
89	C₂×C₃×C₄×C₅	—	4	1	no	—
90	C₂×C₃×C₄×C₅	—	4	1	no	—
91	C₂×C₃×C₄×C₅	—	4	1	no	—
92	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₃×C₅×C₈	—	2	2	no	—
100	C₃×C₅×C₈	—	4	1	no	—
101	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
102	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
103	C₂×C₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
105	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
106	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
107	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
108	C₂×C₃×C₄²	—	2	1	no	—
109	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
110	C₃×#107	C₄×C₅	1	4	yes	complemented
111	C₃×#95	—	2	1	no	—
112	C₃×#95	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
120	C₂×C₅×C₈	—	2	1	no	—
121	C₂×C₅×C₈	—	2	1	no	—
122	C₂×C₅×C₈	—	2	1	no	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
126	C₅×C₄⋊C₄	—	2	1	no	—
127	C₅×C₄⋊C₄	—	2	1	no	—
128	C₅×C₄⋊C₄	—	2	1	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	4	2	no	—
132	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
133	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
134	C₅×C₄⋊C₄	C₃×Q₈	1	2	yes	—
135	C₄²×C₅	—	2	1	no	—
136	C₄²×C₅	—	2	1	no	—
137	C₄²×C₅	—	4	2	no	—
138	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic
139	#389	C₂×C₃×C₅	1	1	yes	characteristic
140	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
141	#340	C₂×C₃×C₅	1	1	yes	characteristic
142	#340	C₂×C₃×C₅	1	1	yes	characteristic
143	#340	C₂×C₃×C₅	1	1	yes	characteristic
144	#336	C₂×C₃×C₅	1	1	yes	characteristic
145	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
146	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
147	C₂²×C₃×C₅	#123	1	1	yes	characteristic
148	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
149	C₂²×C₃×C₅	#135	1	1	yes	characteristic
150	C₂²×C₃×C₅	#137	1	1	yes	characteristic
151	C₂²×C₃×C₅	#137	1	1	yes	characteristic
152	C₃×C₄×C₅	—	2	2	no	—
153	C₃×C₄×C₅	—	4	2	no	—
154	C₃×C₄×C₅	—	4	2	no	—
155	C₃×C₄×C₅	—	4	2	no	—
156	C₃×C₄×C₅	—	4	1	no	—
157	C₃×C₄×C₅	—	8	1	no	—
158	C₃×C₄×C₅	#117	1	1	yes	characteristic
159	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
160	C₃×C₄×C₅	#125	1	1	yes	characteristic
161	C₃×C₄×C₅	#126	1	1	yes	characteristic
162	C₂²×C₃×C₄	—	2	1	no	—
163	C₂²×C₃×C₄	—	2	1	no	—
164	C₂²×C₃×C₄	—	2	1	no	—
165	C₂²×C₃×C₄	—	2	1	no	—
166	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
169	C₂×C₃×C₈	—	2	1	no	—
170	C₂×C₃×C₈	—	2	1	no	—
171	C₂×C₃×C₈	—	2	1	no	—
172	C₂×C₃×C₈	—	2	1	no	—
173	C₂×C₃×C₈	—	2	1	no	—
174	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
175	C₃×C₄⋊C₄	—	2	1	no	—
176	C₃×C₄⋊C₄	—	2	1	no	—
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	—	2	1	no	—
179	C₃×C₄⋊C₄	—	2	1	no	—
180	C₃×C₄⋊C₄	—	4	2	no	—
181	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
182	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
183	C₃×C₄⋊C₄	C₅×Q₈	1	2	yes	—
184	C₃×C₄²	—	2	1	no	—
185	C₃×C₄²	—	2	1	no	—
186	C₃×C₄²	—	4	2	no	—
187	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	—	4	1	no	—
198	C₂×C₄×C₅	—	4	1	no	—
199	C₂×C₄×C₅	—	4	1	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	1	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	C₃×D₈	1	2	yes	—
206	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
208	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
209	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
210	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
211	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
212	C₅×C₈	—	2	2	no	—
213	C₅×C₈	—	4	1	no	—
214	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
215	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
216	C₂×C₄⋊C₄	—	2	1	no	—
217	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
221	C₂×C₄²	—	2	1	no	—
222	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
223	#107	C₃×C₄×C₅	1	4	yes	complemented
224	#95	—	2	1	no	—
225	#95	—	2	1	no	—
226	C₂×C₃×C₅	#387	1	1	yes	characteristic
227	C₂×C₃×C₅	C₄×D₈	1	1	yes	characteristic
228	C₂×C₃×C₅	#441	1	1	yes	characteristic
229	C₂×C₃×C₅	#474	1	1	yes	characteristic
230	C₂×C₃×C₅	#479	1	1	yes	characteristic
231	C₂×C₃×C₅	#480	1	1	yes	characteristic
232	C₂×C₃×C₅	#485	1	1	yes	characteristic
233	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	4	1	no	—
243	C₂×C₃×C₄	—	4	1	no	—
244	C₂×C₃×C₄	—	4	1	no	—
245	C₂×C₃×C₄	—	4	1	no	—
246	C₂×C₃×C₄	—	4	1	no	—
247	C₂×C₃×C₄	—	4	1	no	—
248	C₂×C₃×C₄	—	4	1	no	—
249	C₂×C₃×C₄	—	4	1	no	—
250	C₂×C₃×C₄	—	4	1	no	—
251	C₂×C₃×C₄	C₅×D₈	1	2	yes	—
252	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
254	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
255	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
256	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
257	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
258	C₃×C₈	—	2	2	no	—
259	C₃×C₈	—	4	1	no	—
260	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
261	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
262	C₂²×C₅	C₃×#123	1	1	yes	characteristic
263	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
264	C₂²×C₅	C₃×#135	1	1	yes	characteristic
265	C₂²×C₅	C₃×#137	1	1	yes	characteristic
266	C₂²×C₅	C₃×#137	1	1	yes	characteristic
267	C₄×C₅	—	2	2	no	—
268	C₄×C₅	—	4	2	no	—
269	C₄×C₅	—	4	2	no	—
270	C₄×C₅	—	4	2	no	—
271	C₄×C₅	—	4	1	no	—
272	C₄×C₅	—	8	1	no	—
273	C₄×C₅	C₃×#117	1	1	yes	characteristic
274	C₄×C₅	C₃×C₄×Q₈	1	1	yes	characteristic
275	C₄×C₅	C₃×#125	1	1	yes	characteristic
276	C₄×C₅	C₃×#126	1	1	yes	characteristic
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
282	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
283	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	C₂×C₃×C₄×C₅	1	2	yes	—
297	C₄⋊C₄	C₂×C₃×C₄×C₅	1	2	yes	—
298	C₄⋊C₄	C₃×C₅×Q₈	1	2	yes	—
299	C₄²	—	2	1	no	—
300	C₄²	—	2	1	no	—
301	C₄²	—	4	2	no	—
302	C₃×C₅	#1918	1	1	yes	characteristic, direct product factor, Hall
303	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
304	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
305	C₂²×C₃	C₅×#123	1	1	yes	characteristic
306	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
307	C₂²×C₃	C₅×#135	1	1	yes	characteristic
308	C₂²×C₃	C₅×#137	1	1	yes	characteristic
309	C₂²×C₃	C₅×#137	1	1	yes	characteristic
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	4	2	no	—
312	C₃×C₄	—	4	2	no	—
313	C₃×C₄	—	4	2	no	—
314	C₃×C₄	—	4	1	no	—
315	C₃×C₄	—	8	1	no	—
316	C₃×C₄	C₅×#117	1	1	yes	characteristic
317	C₃×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
318	C₃×C₄	C₅×#125	1	1	yes	characteristic
319	C₃×C₄	C₅×#126	1	1	yes	characteristic
320	C₂×C₅	C₃×#387	1	1	yes	characteristic
321	C₂×C₅	C₃×C₄×D₈	1	1	yes	characteristic
322	C₂×C₅	C₃×#441	1	1	yes	characteristic
323	C₂×C₅	C₃×#474	1	1	yes	characteristic
324	C₂×C₅	C₃×#479	1	1	yes	characteristic
325	C₂×C₅	C₃×#480	1	1	yes	characteristic
326	C₂×C₅	C₃×#485	1	1	yes	characteristic
327	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	C₃×C₅×D₈	1	2	yes	—
346	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
347	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
348	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
349	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
350	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
351	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
352	C₈	—	2	2	no	—
353	C₈	—	4	1	no	—
354	C₂×C₃	C₅×#387	1	1	yes	characteristic
355	C₂×C₃	C₄×C₅×D₈	1	1	yes	characteristic
356	C₂×C₃	C₅×#441	1	1	yes	characteristic
357	C₂×C₃	C₅×#474	1	1	yes	characteristic
358	C₂×C₃	C₅×#479	1	1	yes	characteristic
359	C₂×C₃	C₅×#480	1	1	yes	characteristic
360	C₂×C₃	C₅×#485	1	1	yes	characteristic
361	C₅	C₃×#1918	1	1	yes	characteristic, direct product factor, Sylow
362	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
363	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
364	C₂²	C₃×C₅×#123	1	1	yes	characteristic
365	C₂²	C₂×C₃×C₅×D₈	1	1	yes	characteristic
366	C₂²	C₃×C₅×#135	1	1	yes	characteristic
367	C₂²	C₃×C₅×#137	1	1	yes	characteristic
368	C₂²	C₃×C₅×#137	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	—	8	1	no	—
375	C₄	C₃×C₅×#117	1	1	yes	characteristic
376	C₄	C₃×C₄×C₅×Q₈	1	1	yes	characteristic
377	C₄	C₃×C₅×#125	1	1	yes	characteristic
378	C₄	C₃×C₅×#126	1	1	yes	characteristic
379	C₃	C₅×#1918	1	1	yes	characteristic, direct product factor, Sylow
380	C₂	C₃×C₅×#387	1	1	yes	characteristic
381	C₂	C₃×C₄×C₅×D₈	1	1	yes	characteristic
382	C₂	C₃×C₅×#441	1	1	yes	characteristic
383	C₂	C₃×C₅×#474	1	1	yes	characteristic
384	C₂	C₃×C₅×#479	1	1	yes	characteristic
385	C₂	C₃×C₅×#480	1	1	yes	characteristic
386	C₂	C₃×C₅×#485	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
8. C₅×#1918	C₃	direct (N × H)
18. C₃×C₅×#107	C₄	semidirect
21. C₃×#1918	C₅	direct (N × H)
70. C₅×#107	C₃×C₄	semidirect
73. #1918	C₃×C₅	direct (N × H)
110. C₃×#107	C₄×C₅	semidirect
223. #107	C₃×C₄×C₅	semidirect
302. C₃×C₅	#1918	direct (N × H)
361. C₅	C₃×#1918	direct (N × H)
379. C₃	C₅×#1918	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#107	2
C₃×C₅×#389	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₅×#340	2
C₃×C₅×#336	2
C₅×#1918	3
C₃×#1918	5

Subgroups — C3×C5×#1918 #14274952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1918 #14274952